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# Vx and Vy

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# Vx and Vy

15th Sep 2008, 10:00

Join Date: Nov 2006
Location: Tropics
Posts: 305
Vx and Vy

Hi guys,

I can't really get my head around one question regarding Vx and Vy. How does Vx and Vy vary with altitude? Is there a difference to the answer if we compare it to turbo-props and jets?

The answer I was told is Vx remains constant while Vy decreases.

To my understanding Vx and Vy is TAS. As altitude increases the density of air decreases and so thrust decreases. Therefore climb gradient decreases. To compensate and try to get back the best gradient thus wouldn't it be a reduction of speed to give a better climb gradient?

Why does Vy decreases with altitude? As density decreases thrust decreases thus power available decreases so rate of climb reduces. But I can't see how reducing Vy can give a better climb rate?

Thanks in advance! A bit confusing...
15th Sep 2008, 20:49

Join Date: Oct 2005
Location: USA
Posts: 3,218
The answer is hard to understand until you remember that Vx and Vy are performance numbers based on excess power. The ability of an airplane to climb in still air (disregarding thermal lift or orographic lift from mountains, etc) is dependent on excess power beyond that required to sustain level flight, at a given airspeed. This means, for example that at 100 knots in level flight at 50% power, adding more power either means we go faster, or if we maintain 100 knots, we climb. Climb performance, then, is a function of excess thrust.

As you know, climb speeds such as Vx and Vy have a lot to do with angle of attack and drag. In a light airplane where we don't have an indication of angle of attack, we base our understanding of it in part on airspeed. You're familiar with the drag curve and the power required curves. You understand the differences between Vx and Vy and what they do. The only mystery, then, is why the numbers decrease with altitude.

First of all, remembering that power equals climb performance, we know there's some point in the climb where we're going to run out of power and performance. We just can't climb any more. We've reached the absolute ceiling. At this point, there's just one angle of attack at which we can maintain level flight on the power we've got...pitch up any more, and the airplane descends. Pitch down, and the airplane descends. Vx and Vy have come together. But why?

The only answer can be that power changes a we climb. The rate at which Vx and Vy come together is a function of the power available...and this depends on how we get that power to a useable state of thrust. The engine loses power as it climbs. As air density decreases, manifold pressure decreases (talking about a normally aspirated airplane here, for simplicity), and so forth. You're already familiar with that. Also as the airplane climbs and density decreases, propeller efficiency decreases (let's use a fixed pitch propeller for simplicity, here). In a typical light airplane, climbing only a few thousand feet has already decreased engine output by 25% or so...which is part of the reason that manufacturers generally recommend against leaning below three or four thousand feet...they're idiot proofing to some degree the process by asking you not to lean until you're at an altitude where there's far less chance of hurting the engine. When you've climbed just a few thousand feet and there's less power, the distance between Vx and Vy begins to decrease...with less and less power there's less and less difference between the two...until we reach a point at the absolute ceiling where the airplane can only maintain altitude at one angle of attack...there's no separation between them.

It's important to note that at the absolute ceiling when one can fly a single angle of attack to maintain altitude on one engine...one isn't going to stall...the ceiling is determined by available power...not by the airplane reaching a point where it's run out of wing or the ability to produce lift. When one is barely able to maintain altitude at the absolute ceiling, one isn't on the edge of a stall...on has simply run out of power. As an example, I've flown airplanes well above their ceiling when experimenting before, strictly using thermal and other lift...when no more engine power was available to lift the airplane any higher...the airplane still flies just fine, and will keep on climbing and flying on other forms of lift such as a mountain wave or rising air...it's just run out of engine power to make it go any higher.

You mentioned Vx staying the same and Vy decreasing. Not so. Vx increases with altitude, and Vy decreases. They don't increase and decrease at the same rate, however.

As a ballpark rule of thumb, in a light, normally aspirated, reciprocating-engine airplane, you can reduce both Vx and Vy by about one knot for each 100 lbs of aircraft weight below the max gross takeoff weight. You can do this because usually Vx and Vy are published for maximum weight at sea level...and the airplane climbs better when it's lighter, and has excess thrust available that's not needed to matain level flight...every pound or kg lighter means more available thrust, means more available climb performance, and this takes place at a different speed...about 1 knot less per 100 lbs of weight.

Vy may also be reduced about 1% for each 1,000' of density altitude. Roughed out, this still amounts to about 1 knot per thousand feet. Vx doesn't decrease, however. It increases with altitude. Of interest, you'll probably find the Vx numbers in your handbook published for a short field takeoff, which is done with flaps down...but you probably won't find the numbers published for Vx with flaps up...and Vx differs between flaps down and flaps up...just as the power to sustain level flight differs with flaps down or flaps up...and thus any excess power beyond that differs between flaps down or up.

If that data isn't available, you can make it for yourself with some experimentation. You can do that by making a series of climbs at differing airspeeds and noting the performance on your vertical speed indicator, and repeating it at increasing altitudes to see what happens.

A ballpark rule for Vx is that it increases about 1/2 percent per thousand feet of altitude increase. Whereas Vy decreases (again, normally aspirated piston powered airplane, here, with a fixed pitch prop) by 1%, Vx increases by 1/2 percent...or about 1 knot per two thousand feet of density altitude increase.

If the temperature change remains constant and linear with a climb to altitude the change in Vx and Vy with altitude also remains fairly constant...so that if you know your sea level numbers and you know your service ceiling numbers, you can interpolate fairly accurately what the Vx and Vy numbers are for all the altitudes in between.

If you change the situation by turbocharging or using a turbine engine, it becomes a little more complicated, because the way the power changes with altitude is affected, and the rates of change therefore also affected.
15th Sep 2008, 21:43

Join Date: Aug 2005
Location: Estonia
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Maybe it could be easier to consider for the start unpowered flight.

For a glider, the best glide AoA and best glide L/D and IAS should be independent of density and TAS - so long as the TAS remains low in terms of Mach number.

For any given air density, there should be some AoA, IAS and TAS, lower than the best glide AoA, where the sink rate is slowest. The slowest sink IAS and TAS should be slower than the best glide speed.

As the glider flies higher, its L/D, best glide IAS and slowest sink IAS should stay unchanged. But its best glide TAS, slowest sink TAS and slowest sink rate should increase with decreasing density.

How does existence of engines change this?
15th Sep 2008, 22:11

Join Date: Oct 2005
Location: USA
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Because climb performance is a function of power, and the change in Vx and Vy is a function in the change in available thrust with an increase in density altitude.
15th Sep 2008, 23:49

Join Date: Sep 2008
Location: Asia
Posts: 77
Vx = Best angle of climp....getting over those hills up ahead.. For a given distance, rise over run. Techinicaly Vx should decrease as well, unless I am missing something. Vy = Best rate of climb...the most VSI you can get up to alt...the higher you go, the thinner the air, the less engine performance, Vy decreases with altitude, as engine performance decreases....
16th Sep 2008, 06:36

Join Date: Oct 2005
Location: USA
Posts: 3,218
Techinicaly Vx should decrease as well, unless I am missing something.
Oh, you are.

Vx increases with altitude, in a normally aspirated reciprocating powered fixed pitch airplane. As indicated before, it increases approximately .5% per thousand feet of density altitude.

Vy decreases, Vx increases, and they meet at the absolute ceiling.
16th Sep 2008, 11:24

Join Date: Nov 2006
Location: Tropics
Posts: 305
Hi Guppy,

First of all thanks a million for such an informative post. All that you've written made perfect sense to me and I could understand it, hopefully in a correct way. However I'm still a bit blurred by the direct relation to the mentioned V speeds.

To be it into use, for example lets assume my Vx is 100 knots (just want to reconfirm this is TAS and not CAS/EAS/IAS?) right after departure. As I climb towards the sky my excess power drops because of all the reasons you've stated above. Can't I then, reduce from 100 knots to compensate and give a better climb gradient as compared to what I would have should I continue the climb at 100 knots? Wouldn't that make Vx decrease?

Which part of this whole concept am I not getting it right?

Last edited by dream747; 16th Sep 2008 at 11:25. Reason: Spelling
16th Sep 2008, 13:30

Join Date: Apr 2003
Location: orbital
Posts: 186
Dream, reducing IAS means pitching up, which means the component of aircraft weight opposite to the flight path increases, thus reducing the excess power available.

Think about pointing at the sky. Then you're going backwards (unless you're in an F-16).

Good explanation of this here

Last edited by Re-entry; 17th Sep 2008 at 05:30.
16th Sep 2008, 14:34

Join Date: Aug 2005
Location: Estonia
Posts: 834
reducing IAS means pitching up, which means the component of aircraft weight opposite to the flight path increases, thus reducing the excess power available.
Think about pointing at the sky. Then your going backwards (unless you're in an F-16).
Or a helicopter.

Helicopters often have nonzero climb rate at zero TAS, and therefore zero Vx. But they commonly have climb rate at some nonzero TAS that exceeds climb rate at zero TAS, and thus they possess nonzero Vy. They also have higher ceilings at nonzero TAS than at zero TAS - and therefore for a certain height range possess nonzero Vx in addition to a nonzero Vy.
16th Sep 2008, 16:36

Join Date: Aug 2000
Location: UK
Posts: 3,644
Here's the way I look at it:

Vy is the speed of maximum excess power = power available - power required. If power available were not a function of speed, that would be the same as minimum power required speed (minimum sink rate for a glider). But since power available increases with speed, Vy occurs at a higher speed than minimum power required. As the power available reduces with altitude, Vy reduces to much closer to the minimum power required speed at the absolute ceiling of the aircraft.

Vx is the speed of maximum excess thrust = thrust available - thrust required (drag). If thrust available were not a function of speed, that would be the same as minimum drag speed (best glide for a glider). But since thrust available decreases with speed, Vx occurs at a lower speed than minimum drag speed. As the thrust available reduces with altitude, Vx increases to much closer to the minimum drag speed at the absolute ceiling of the aircraft.

You ask about the difference between props and jets. Props are closer to constant power systems -- thrust reduces significantly with speed, and so the effect increasing Vx is more significant than the decrease in Vy. Jets are closer to constant thrust systems -- power increases significantly with speed, and so the effect decreasing Vy is more significant than the increase in Vx. Both of those are simplifications: in fact thrust decreases and power increases with speed for both props and jets.

There's one more complication which is that the power required is a function of both IAS/CAS because it depends on drag, and TAS because power is drag times (true) speed. As altitude increases and TAS increases for a given IAS, the minimum power required will reduce. This effect will tend to reduce Vy with altitude, even for an engine that doesn't care so much about the thinner air.
17th Sep 2008, 00:53

Join Date: Nov 2006
Location: Tropics
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Thanks everyone for chipping in. After some thinking through and reasoning the graph from the link by re-entry got me through.

Really appreciate it. Fly safe guys!
17th Sep 2008, 15:54

Join Date: Aug 2005
Location: Estonia
Posts: 834
Vx is the speed of maximum excess thrust = thrust available - thrust required (drag). If thrust available were not a function of speed, that would be the same as minimum drag speed (best glide for a glider). But since thrust available decreases with speed, Vx occurs at a lower speed than minimum drag speed. As the thrust available reduces with altitude, Vx increases to much closer to the minimum drag speed at the absolute ceiling of the aircraft.
Jets are closer to constant thrust systems -- power increases significantly with speed, and so the effect decreasing Vy is more significant than the increase in Vx. Both of those are simplifications: in fact thrust decreases and power increases with speed for both props and jets.

There's one more complication which is that the power required is a function of both IAS/CAS because it depends on drag, and TAS because power is drag times (true) speed. As altitude increases and TAS increases for a given IAS, the minimum power required will reduce. This effect will tend to reduce Vy with altitude, even for an engine that doesn't care so much about the thinner air.
Disagreed.

Imagine that you had an engine which offered constant thrust completely independent of speed or altitude. Such engines exist. Namely rockets.

If you start flying a rocket powered plane at, say, IAS and TAS of 50 knots, you would have some speed for stall, another speed for zero rate of climb, then Vx speed, then Vy speed (and associated maximum climb rate), then maximum speed for sustained level flight. Now go on and climb into stratosphere. When your speed is 250 knots TAS and still 50 kn IAS, your Vs, Vzrc, Vx, L/Dmax, Vy and Vmax would, in terms of IAS, be unchanged. It terms of TAS, they will have increased fivefold And your maximum climb rate also has increased 5 times.

The same applies when your speed is 500 knots TAS, except that Mach effects will affect the actual shape of polar curve (and your best L/D worsens with sound barrier wave drag). As well as at 5000 kn TAS (except that the hypersonic effects lead to further deterioration of L/D). As you approach 15 000 kn ground speed, centrifugal forces increase and your weight vanishes.

So - for an engine whose thrust is constant, there is no such a thing as ceiling.

Now, if you have an engine whose thrust DOES derate with altitude and airspeed, because it does take in air, as the plane climbs towards it ceiling, in terms of IAS we can expect that Vs would be unchanged, Vzrc and Vx would increase, while Vy and Vmax would decrease. Above the ceiling, the whole polar curve would be below zero, Vs would be unchanged, there would be no Vzrc or Vmax (no crossing of polar curve and zero rate of climb), and there would be Vy and Vx - with Vy smaller than Vx.

And exactly at the ceiling, the polar curve would touch the zero rate of climb at one speed, which is equally Vzrc, Vx, Vy and Vmax.

I should expect Vy to decrease with altitude in terms of IAS. But what should happen to Vy in TAS terms? I see no reason why a plane whose thrust does decrease with speed and altitude, but does so only slowly (low-bypass turbofan, afterburner...) could not have TAS Vy increasing all the way to its ceiling where it is overtaken by Vx?
18th Sep 2008, 04:01

Join Date: Aug 2003
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Off thread and just to be a pain
Imagine that you had an engine which offered constant thrust completely independent of speed or altitude. Such engines exist. Namely rockets.
From the formula you will see that a rockets thrust in a vacuum (space) will be greater than at sea level. As a rocket climbs the ambient pressure progressively reduces until you reach space where it becomes effectively zero (space is not a perfect vacuum).

Gross thrust = Fn = mVe+ Ae(Pe - Pamb)

where:

m = propellant flow (kg/s or lb/s)

Ve = jet velocity at nozzle exit plane (m/s or s)

Ae = flow area at nozzle exit plane (m2 or ft2)

Pe = static pressure at nozzle exit plane (Pa or lb/ft2)

Pamb = ambient (or atmospheric) pressure (Pa or lb/ft2)

18th Sep 2008, 13:49

Join Date: Aug 2000
Location: UK
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Disagreed.
Er, OK, but I haven't worked out what you're disagreeing with.

I should expect Vy to decrease with altitude in terms of IAS. But what should happen to Vy in TAS terms? I see no reason why a plane whose thrust does decrease with speed and altitude, but does so only slowly (low-bypass turbofan, afterburner...) could not have TAS Vy increasing all the way to its ceiling where it is overtaken by Vx?
Sure, but V-speeds are IAS (or CAS) not TAS. The TAS corresponding to Vy may well increase. In the case of a constant thrust jet, both power required and power available have a dependence on the TAS, so Vy may remain constant in EAS, with the TAS corresponding to it increasing with altitude.
18th Sep 2008, 17:47

Join Date: Aug 2005
Location: Estonia
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Sure, but V-speeds are IAS (or CAS) not TAS.
The first time anyone said so in this thread.

From the original post:
To my understanding Vx and Vy is TAS.
and later
(just want to reconfirm this is TAS and not CAS/EAS/IAS?)
19th Sep 2008, 17:05

Join Date: Aug 2000
Location: UK
Posts: 3,644
Ah, I see what you mean chornedsnorkack.

FAR 23.51 and 25.107 define a number of speeds (e.g. V1, V2, VR, VMU, and elsewhere VS0, VS1) explicitly as calibrated (not true) speeds. Though FAR 1 defines many more speeds, including those and VX/VY, I can't find anything that definitively states that VX and VY are calibrated speeds, and in fact I can't see any requirement to list VX/VY in the AFM. Nevertheless, I've always assumed that any 'V'-speeds are intended as calibrated/indicated speeds, not TAS.
20th Sep 2008, 00:44

Join Date: Apr 2004
Location: London
Posts: 490
chornedsnorkack, the speeds are initially established using either TAS or EAS and are finally expressed in CAS. If you want a thorough academic treatment of this subject I would suggest Nguyen X. Vinh's Flight Mechanics of High-Performance Aircraft.
20th Sep 2008, 04:47

Join Date: Nov 2006
Location: Tropics
Posts: 305
http://www.pprune.org/tech-log/86413-v-speeds.html

I see from here that Vx and Vy are part of the other V speeds which are IAS or CAS so I'd presume so would Vx and Vy!
30th May 2010, 17:12

Join Date: Apr 2008
Location: SFO
Posts: 21
So I am sitting here in my hotel room this morning in Carson City, Nevada, thinking about my departure this afternoon with my family in an old 1970 Piper Arrow.

My planned departure is going to be around 3pm. The forecast for that time says around 70 degrees. Yesterday's weather history showed one point at 70.3 degrees, 32.8 degree dew point and 30.1 inches. CXP is 4700'. I calculated density altitude to be 6360' - call it 6500'. The charts at MGTW show the ground roll at 1550' w/25 degrees of flaps and 2100' clean. Over 50' it is 3600' and 4000' respectively. CXP is 6100'.

I am 300lbs under gross and the rising terrain is high but in the distance so I am thinking a clean takeoff to get to Vy quickly then a slow left turnout past 1000' AGL.

Vy is 100mph, Vx 95 (Pretty close eh?). Using the information above, I am thinking that Vy is reduced by 3kts for the weight and another 6.5kts for the DA. So 9.5kts total, or 11mph. This should give me Vy of 90mph. Does this sound right?

I think I should be fine today (POH says 550fpm at mgtw at 6500'), but I am always weary of taking off high and warm, especially with my family. I have done Truckee several times and South Lake Tahoe (One memorable Summer experience with a gusty Southerly wind - that place eats airplanes...). so I familiar with the trees not getting smaller that quickly.

The Arrow really does feel like a brick on takeoff at altitude without flaps. Not at all like a Bonanza.

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